Thank you for your review. I was also searching for a replacement for FavIcon Reloader and every thread on favicon-reloading led the the same answer: Click "Open All in Tabs.." for each bookmarks-folder. The WebExtensions API does not support favicon reloading/manipulation.

Another workaround: You can run this addon in the background if you open another browser window where you can also close the sidebar. The addon loads tabs only in the window it was started in...